Remark 4.1.7 
lemma:positive-Hodge-bundle is essentially due to Griffiths in the case of real variations of
Hodge structure on a
smooth proper curve. In that case it follows from the curvature formula [1]}, and is observed there in some special cases
[1]}. For a more precise
reference, see [3]}, which
immediately implies the claim for real variations of Hodge structure on a smooth proper curve.
However, as we were unable to find a precise reference in the case of complex
variations on a quasi-projective curve, we now give a simple proof.
An similar argument is given in the proof of
[4]}.

